A comparison of the spectral characteristics of the Wolf Sunspot Number (R Z) and Group Sunspot Number (R G)

The objective of this paper is to compare the spectral features of the recently derived Group Sunspot Numbers (R _G) and the traditional Wolf Sunspot Numbers (R _Z) for the 1700–1995 period. In order to study the spectral features of both time series, two methods were used, including: (a) the multitaper analysis and (b) the wavelet analysis. Well-known features of the solar variability, such as the 98.6-yr (Gleissberg cycle), 10–11-yr (Schwabe cycle) and 5-yr (second solar harmonic) periodicities were identified with high confidence using the multitaper analysis. Also observed was a larger amount of power spread in high frequencies for R _Z than for R _G spectra. Furthermore, a multitaper analysis of two subsets, A (1700–1850) and B (1851–1995), has indicated that the main differences occurred in the first subset and seem to be due to uncertainties in the early observations. The wavelet transform, which allows observing the spectra evolution of both series, showed a strong and persistent 10–11-yr signal that remained during the whole period. The Meyer Wavelet Transform was applied to both R _Z and R _G. This study indicates that the main spectral characteristics of both series are similar and that their long-term variability has the same behavior.     

A comparison of the spectral characteristics of the Wolf Sunspot Number (RZ) and Group Sunspot Number (RG)

The objective of this paper is to compare the spectral features of the recently derived Group Sunspot Numbers (R _G) and the traditional Wolf Sunspot Numbers (R _Z) for the 1700–1995 period. In order to study the spectral features of both time series, two methods were used, including: (a) the multitaper analysis and (b) the wavelet analysis. Well-known features of the solar variability, such as the 98.6-yr (Gleissberg cycle), 10–11-yr (Schwabe cycle) and 5-yr (second solar harmonic) periodicities were identified with high confidence using the multitaper analysis. Also observed was a larger amount of power spread in high frequencies for R _Z than for R _G spectra. Furthermore, a multitaper analysis of two subsets, A (1700–1850) and B (1851–1995), has indicated that the main differences occurred in the first subset and seem to be due to uncertainties in the early observations. The wavelet transform, which allows observing the spectra evolution of both series, showed a strong and persistent 10–11-yr signal that remained during the whole period. The Meyer Wavelet Transform was applied to both R _Z and R _G. This study indicates that the main spectral characteristics of both series are similar and that their long-term variability has the same behavior.     

Can the Solar Cycle Amplitude Be Predicted Using the Preceding Solar Cycle Length?

In this work, the evolution of the relationship between Solar Cycle Length of solar cycle n (SCL _n ) and Solar Cycle Amplitude of the solar cycle n+1 (SCA _n+1) is studied by using the R _Z and R _G sunspot numbers. We conclude that this relationship is only strongly significant in a statistical sense during the first half of the historical record of R _Z sunspot number whereas it is considerably less significant for the R _G sunspot number. In this sense we assert that these simple lagged relationships should be avoided as a valid method to predict the following solar activity amplitude.     

A Note on Solar Cycle Length Estimates

Recently, new estimates of the solar cycle length (SCL) have been calculated using the Zurich Sunspot Number (R_Z) and the Regression-Fourier-Calculus (RFC)-method, a mathematically rigorous method involving multiple regression, Fourier approximation, and analytical expressions for the first derivative. In this short contribution, we show estimates of the solar cycle length using the RFC-method and the Group Sunspot Number (R_G) instead the R_Z. Several authors have showed the advantages of R_G for the analysis of sunspot activity before 1850. The use of R_G solves some doubtful solar cycle length estimates obtained around 1800 using R_Z.     

Some notes concerning the prediction of the amplitude of the solar activity cycles

The parameter G, which is determined from the general number of sunspots groups N _g according to the daily observations G=∑(1/N _g )², is offered. This parameter is calculated for the days when there is at least one sunspots group. It characterizes the minimum epoch solar activity. Parameter G mounts to the maximum during the epoch close to the minimal activity of sunspots. According to the data of the sequence of sunspots group in Greenwich–USAF/NOAA observatory format, observation data of Kislovodsk solar station and also daily Wolf number, the changes of parameter G during 100 years were reconstructed. It is demonstrated in the paper that parameter G’s amplitude in minimal solar activity n is linked with the sunspot cycle’s amplitude W _n+1 or one and half cycles. The 24th activity cycle prediction is calculated, which makes W ₂₄=135(±12).     

Two Early Sunspots Observers: Teodoro de Almeida and José Antonio Alzate

We present the sunspot ideas and observations of the 18th century Portuguese scholar Teodoro de Almeida (1722 – 1804) and Mexican scientist José Antonio Alzate (1737 – 1799). We describe the implications of dating a single sunspot observation performed by Almeida in the early 1760s, during the maximum of cycle number 1. A possible solar cycle peak in 1760 (instead of 1761) is investigated. We present several observations of sunspots obtained by Alzate during 1769 (partially associated with the Venus and Mercury transits) and also on 20 July 1786. We estimate 100±34 as the Group Sunspot Number for this date. These records were unknown and, therefore, not included in the database compiled by Hoyt and Schatten (1998).     

Interplanetary magnetic field structure and solar wind parameters as inferred from solar magnetic field observations and by using a numerical 2-D MHD model

An attempt is made to infer parameters of the solar corona and the solar wind by means of a numerical, self-consistent MHD simulation. Boundary conditions for the magnetic field are given from the observations of the large-scale magnetic field at the Sun. A two-region, planar (the ecliptic plane is assumed) model for the solar wind flow is considered. Region I of transonic flow is assumed to cover the distances from the solar surface up to 10R _S (R _S is the radius of the Sun). Region II of supersonic, super-Alfvénic flow extends between 10R _S and the Earth's orbit. Treatment for region I is that for a mixed initial-boundary value problem. The solution procedure is similar to that discussed by Endler (1971) and Steinolfson, Suess, and Wu (1982): a steady-state solution is sought as a relaxation to the dynamic equilibrium of an initial state. To obtain a solution to the initial value problem in region II with the initial distribution of dependent variables at 10R _S (deduced from the solution for region I), a numerical scheme similar to that used by Pizzo (1978, 1982) is applied. Solar rotation is taken into account for region II; hence, the interaction between fast and slow solar wind streams is self-consistently treated. As a test example for the proposed formulation and numerical technique, a solution for the problem similar to that discussed by Steinolfson, Suess, and Wu (1982) is obtained. To demonstrate the applicability of our scheme to experimental data, solar magnetic field observations at Stanford University for Carrington rotation 1682 are used to prescribe boundary conditions for the magnetic field at the solar surface. The steady-state solution appropriate for the given boundary conditions was obtained for region I and then traced to the Earth's orbit through region II. We compare the calculated and spacecraft-observed solar wind velocity, radial magnetic field, and number density and find that general trends during the solar rotation are reproduced fairly well although the magnitudes of the density in comparison are vastly different.     

Coronal Field Opens at Lower Height During the Solar Cycles 22 and 23 Minimum Periods: IMF Comparison Suggests the Source Surface Should Be Lowered

The solar cycle 23 minimum period has been characterized by a weaker solar and interplanetary magnetic field. This provides an ideal time to study how the strength of the photospheric field affects the interplanetary magnetic flux and, in particular, how much the observed interplanetary fields of different cycle minima can be understood simply from differences in the areas of the coronal holes, as opposed to differences in the surface fields within them. In this study, we invoke smaller source surface radii in the potential-field source-surface (PFSS) model to construct a consistent picture of the observed coronal holes and the near-Earth interplanetary field strength as well as polarity measurements for the cycles 23 and 22 minimum periods. Although the source surface value of 2.5 R _⊙ is typically used in PFSS applications, earlier studies have shown that using smaller source surface heights generates results that better match observations during low solar activity periods. We use photospheric field synoptic maps from Mount Wilson Observatory (MWO) and find that the values of ≈ 1.9 R _⊙ and ≈ 1.8 R _⊙ for the cycles 22 and 23 minimum periods, respectively, produce the best results. The larger coronal holes obtained for the smaller source surface radius of cycle 23 somewhat offsets the interplanetary consequences of the lower magnetic field at their photospheric footpoints. For comparison, we also use observations from the Michelson Doppler Imager (MDI) and find that the source surface radius of ≈ 1.5 R _⊙ produces better results for cycle 23, rather than ≈ 1.8 R _⊙ as suggested from MWO observations. Despite this difference, our results obtained from MWO and MDI observations show a qualitative consistency regarding the origins of the interplanetary field and suggest that users of PFSS models may want to consider using these smaller values for their source surface heights as long as the solar activity is low.     

Theoretical emission line ratios for O vii in low-density plasmas

New electron excitation rates for O vii calculated by Tayal and Kingston using the R-matrix method are used to determine theoretical emission line strengths. Values of the electron density sensitive ratio R (forbidden line to intercombination line) are found to be very similar to those deduced by other authors. However the temperature sensitive ratios G (intercombination plus forbidden lines to resonance line) are approximately 20% lower than the best previous estimates. The observed value of G for solar active regions (G = 1.0 ± 0.1) predicts an electron temperature in the range 1.1 × 10⁶ K < T _e < 1.8 × 10⁶ K, which overlaps that of maximum O vii emissivity, T _M = 1.8 × 10⁶ K. In addition, the theoretical G versus T _e curve is in excellent agreement with that observed for a Tokamak plasma.     

Two-Station Interplanetary Scintillation Measurements of Solar Wind Speed near the Sun Using the X-band Radio Signal of the Nozomi Spacecraft

Interplanetary scintillation (IPS) measurements of the solar wind speed for the distance range between 13 and 37 R _S were carried out during the solar conjunction of the Nozomi spacecraft in 2000?–?2001 using the X-band radio signal. Two large-aperture antennas were employed in this study, and the baseline between the two antennas was several times longer than the Fresnel scale for the X-band. We successfully detected a positive correlation of IPS from the cross-correlation analysis of received signal data during ingress, and estimated the solar wind speed from the time lag corresponding to the maximum correlation by assuming that the solar wind flows radially. The speed estimates range between 200 and 540?km?s^?1 with the majority below 400?km?s^?1. We examined the radial variation in the solar wind speed along the same streamline by comparing the Nozomi data with data obtained at larger distances. Here, we used solar wind speed data taken from 327 MHz IPS observations of the Solar-Terrestrial Environment Laboratory (STEL), Nagoya University, and in?situ measurements by the Advanced Composition Explorer (ACE) for the comparison, and we considered the effect of the line-of-sight integration inherent to IPS observations for the comparison. As a result, Nozomi speed data were proven to belong to the slow component of the solar wind. Speed estimates within 30 R _S were found to be systematically slower by 10?–?15 % than the terminal speeds, suggesting that the slow solar wind is accelerated between 13 and 30 R _S.     

Use of Al xii and Mg xi lines as solar plasma diagnostics

We present three sets of observations of n = 1 to n = 2 lines due to helium-like aluminium (Alxii), made during two solar flares (25 August, 1980 and 19 October, 1986), using the X-Ray Polychromator on the SMM satellite. The observed temperature-sensitive line ratio G is shown to be consistent with the close-coupling calculations of Keenan and McCann (1987), although the ratio R, which is both temperature and density-sensitive for lower-Z elements, is not sufficiently well determined from these data to say more than that the observed values of R are not inconsistent with the theoretical calculations. This region of the spectrum also includes the helium-like magnesium (Mgxi) 1¹ S - 3¹ P line, and it is shown that the ratio of this line to the Alxii resonance (1¹ S - 2¹ P) line is a more sensitive indicator of electron temperature than are the Alxii G and R ratios. We demonstrate that the three ratios may be used together in order to derive values of emission measure, electron temperature and electron density during these flares.     

Electron Temperatures and Flow Speeds of the Low Solar Corona: MACS Results from the Total Solar Eclipse of 29 March 2006 in Libya

An experiment was conducted in conjunction with the total solar eclipse on 29 March 2006 in Libya to measure both the electron temperature and its flow speed simultaneously at multiple locations in the low solar corona by measuring the visible K-coronal spectrum. Coronal model spectra incorporating the effects of electron temperature and its flow speed were matched with the measured K-coronal spectra to interpret the observations. Results show electron temperatures of (1.10±0.05) MK, (0.70±0.08) MK, and (0.98±0.12) MK, at 1.1 R _⊙ from Sun center in the solar north, east and west, respectively, and (0.93±0.12) MK, at 1.2 R _⊙ from Sun center in the solar west. The corresponding outflow speeds obtained from the spectral fit are (103±92) km s⁻¹, (0+10) km s⁻¹, (0+10) km s⁻¹, and (0+10) km s⁻¹. Since the observations were taken only at 1.1 R _⊙ and 1.2 R _⊙ from Sun center, these speeds, consistent with zero outflow, are in agreement with expectations and provide additional confirmation that the spectral fitting method is working. The electron temperature at 1.1 R _⊙ from Sun center is larger at the north (polar region) than the east and west (equatorial region).     

The evolution and the secondary maximum of the green line intensity

A new relation has been given in order to calculate the intensity of the green line of the solar corona at 5303 Å as a function of the number of proton events N _P and the R (R) index of solar activity. This relation is available for the 19th and 20th solar cycles. Moreover there is given a theoretical justification of this relationship taking into account as a new parameter the evolution of the coronal magnetic field during the solar cycle.     

Physical observations of (5145) Pholus

We present physical measurements of the newly discovered asteroid, (5145) Pholus, based on seven nights of photometric observations. These observations determine an unambiguous lightcurve period of 9.9825 ± 0.0040 hr with a peak-to-peak amplitude of 0.15 mag. We also report a rotationally independent color of (V − R) = 0.810 ± 0.006 (Kron-Cousins R). The standard IAU two parameter fit versus solar phase angle yields H_V = 7.645 ± 0.011 and G_V = 0.16 ± 0.08. Except for its color and orbit, (5145) Pholus exhibits normal asteroidal properties.     

Twenty-Seven-Day Variation of Galactic Cosmic Rays

Neutron monitor data observed at Climax (CL) and Huancayo/Haleakala (HU/HAL) have been used to calculate the amplitude A of the 27-day variation of galactic cosmic rays (CRs). The median primary rigidity of response, R _m, for these detectors encompasses the range 18 ≤R _m≤46 GV and the threshold rigidity R ₀ covers the range 2.97≤R ₀≤12.9 GV. The daily average values of CR counts have been harmonically analyzed for each Bartels solar rotation (SR) during the period 1953 – 2001. The amplitude of the 27-day CR variation is cross-correlated to solar activity as measured by the sunspot number R, the interplanetary magnetic field (IMF) strength B, the z-component B _z of the IMF vector, and the tilt angle ψ of the heliospheric current sheet (HCS). It is anticorrelated to the solar coronal hole area (CHA) index as well as to the solar wind speed V. The wind speed V leads the amplitude by 24 SRs. The amplitude of the 27-day CR variation is better correlated to each of the these parameters during positive solar polarity (A>0) than during negative solar polarity (A<0) periods. The CR modulation differs during A>0 from that during A<0 owing to the contribution of the z-component of the IMF. It differs during A ₁>0 (1971 – 1980) from that during A ₂>0 (1992 – 2001) owing to solar wind speed.     

The distribution of solar flares for the time period 1967–1985

The distribution of monthly counts of grouped solar flares N _f has been studied for the time period 1967–1985 and they have been compared to other solar activity index R _z , F ₂₈₀₀, and F ₃₇₅₀ i.e. intensities of solar radio flux at 2800 MH _z and 3750 MH _z . Seasonal variations have been found in the monthly distribution of solar flares.We have also studied the variation of the correlation coefficient for every year between N _F and R _z for the time period 1967–1985. The distribution of monthly counts of grouped solar flares N _f has also been compared to the number at high velocity solar-wind streamers for the same period.     

A comparison between estimations of Fried's parameter r o simultaneously obtained by measurements of solar granulation contrast and of the variance of angle-of-arrival fluctuations

Estimations of Fried's parameter r _o are performed simultaneously using the same telescope, from the observed solar granulation contrast and from the variance of angle-of-arrival fluctuations. The results are well correlated and the mean ratio between the values for r _o obtained from the 2 methods is found to be equal to 1.4.The sensitivity and accuracy of the methods are discussed in terms of their range of application (site testing, seeing measurements during solar observations ...). Temporal power spectra of turbulent energy are computed and evidence of long period oscillations of about 10 min is found.     

Evidence for a coronal magnetic bottle at 10 solar radii

The Faraday rotation of a radio source (Pioneer 6) occulted by the solar corona has been measured by Levy et al. (1969). During the course of these measurements, three large-scale transient phenomena were observed. These events were preceded by subflares and class 1 flares. These transient events are interpreted as evidence for a coronal magnetic bottle at 10 R _⊙. The velocity of propagation for the disturbance is set at 200 km/sec; the dimension of the region, 10 R _⊙; field strength at 10 R _⊙, 0.02 G; particle density, 2.0 × 10⁴/cm³; Alfvén speed, 320 km/sec. From the nature of the observations and the lack of related effects from similar flares on the interplanetary sector pattern observed at 1 AU, it is suggested that such coronal magnetic bottles expand to perhaps 10–30 R _⊙ and then contract to a few solar radii. Such a phenomena is evidence for an expansion of the corona with a sub-Alfvénic velocity. It is further suggested that such magnetic bottles may be important in the storage and diffusion of solar generated cosmic ray particles. NAS-NRC Postdoctoral Resident Research Associate.     

The Schwabe and Gleissberg Periods in the Wolf Sunspot Numbers and the Group Sunspot Numbers

Three wavelet functions: the Morlet wavelet, the Paul wavelet, and the DOG wavelet have been respectively performed on both the monthly Wolf sunspot numbers (R_z) from January 1749 to May 2004 and the monthly group sunspot numbers (R_g) from June 1795 to December 1995 to study the evolution of the Gleissberg and Schwabe periods of solar activity. The main results obtained are (1) the two most obvious periods in both the R_z and R_g are the Schwabe and Gleissberg periods. The Schwabe period oscillated during the second half of the eighteenth century and was steady from the 1850s onward. No obvious drifting trend of the Schwabe period exists. (2) The Gleissberg period obviously drifts to longer periods the whole consideration time, and the drifting speed of the Gleissberg period is larger for R_z than for R_g. (3) Although the Schwabe-period values for R_z and R_g are about 10.7 years, the value for R_z seems slightly larger than that for R_g. The Schwabe period of R_z is highly significant after the 1820s, and the Schwabe period of R_g is highly significant over almost the whole consideration time except for about 20 years around the 1800s. The evolution of the Schwabe period for both R_z and R_g in time is similar to each other. (4) The Gleissberg period in R_z and R_g is highly significant during the whole consideration time, but this result is unreliable at the two ends of each of the time series of the data. The evolution of the Gleissberg period in R_z is similar to that in R_g.